You may want to review factoring with GCDs and factoring harder polynomials first.

Polynomials can have GCDs and still start with a number once you've factored it out. For example, consider 6x2 + 16x + 8. The GCD here is 2, so it factors as 2(3x2 + 8x + 4). But the polynomial 3x2 + 8x + 4 itself factors, so the final answer is 2(3x + 2)(x + 2).